Determining the beginning of Ramadan
The obligation of fasting the month of Ramadan begins upon the occurrence of one of two matters:
1. To sight the crescent of Ramadan after the sunset of the 29th day of Sha^ban (the month directly preceding Ramadan) or, if the crescent is not seen,
2. Completing thirty (30) days of Sha^ban.
So, the beginning of the month of Ramadan, as well as the end of the month, is determined by sighting the crescent. If the crescent was not sighted, then the month would be completed by 30 days, as is the case with determining all the months of the lunar calendar. This is taken from the hadith of the Prophet صلى الله عليه وسلّم related by al-Bukhariyy and Muslim:
لا تَقَدَّمُوا رَمَضانَ بِيَومٍ أَوْ يَومَين صُوموا لرؤيتِه وأفطِرُوا لرُؤيتِه فإنْ غُمَّ علَيكم فأكْمِلوا عِدَّةَ شَعبانَ ثلاثينَ يوما
which means: <<Do not fast one or two days before Ramadan. Start the month when you see the crescent, and end it when you see the crescent. If you are blocked from seeing it, then complete thirty days of Sha^ban.>>
So, on the 29th day of Sha^ban, directly after the sun sets, Muslims look towards the western horizon. If the crescent (of the new moon) is seen, the following day will be the first day of Ramadan. If it is not seen, Sha^ban, and the day after that is the first day of Ramadan. If there were to be an Islamic judge, he would confirm the beginning of Ramadan if one upright Muslim, whose testimony is acceptable to the judge, bears witness he saw the crescent.
Several conditions must be met for a person's testimony to be acceptable to the judge in this matter. He must be Muslim, male, pubescent, free, clear of enormous sins, clear of having his sins exceed his acts of obedience, and abiding by the manners of the people of his class. The judge does not confirm the beginning of the month of Ramadan. He does not announce to the general public to commence fasting relying solely upon their testimony. However, if just one upright Muslim, who has satisfied the aforementioned conditions testified to the judge he saw the crescent, the judge would confirm the beginning of Ramadan for the next day. This is known from the hadith related by Abu Dawud from the route of ^Abdullah Ibn ^Umar. ^Abdullah Ibn ^Umar told the Prophet صلى الله عليه وسلّم he had sighted the crescent, so the Prophet صلى الله عليه وسلّم fasted the next day and ordered the others to fast as well. This Hadith was authenticated by Ibn Hibban.
Be warned of those who determine the month of Ramadan relying upon astronomical calculation. Prophet Muhammad صلى الله عليه وسلّم informed us that such calculations are not relied upon in determining such matters. Imam Ahmad may Allah raise his rank related in his Musnad that the Prophet صلى الله عليه وسلّم said:
" نحنُ أمةٌ أميةٌ لا نكتُبُ ولا نحسِبُ الشهرُ هكذا وهكذا "
which means: <<We are a nation which does not depend on writings and calculations [to determine the beginning of the month. The month is either twenty-nine or thirty days.>>
Praise be to Allah سبحانَه وتعالى , how easy the matter is! Any Muslim with sound and proper sight can observe the crescent. He does not need to rely on complex calculations which only a few people understand.